Reliability Based Pseudo-Dynamic Analysis of Gravity Retaining Walls

Abstract

Pseudo-dynamic method of analysis, considering the effect of earthquake loading, shear and primary waves, results in more realistic values of earth pressures than the commonly used pseudo-static method. To account for the uncertainties of geotechnical parameters, conventionally, either a global Factor of Safety (FS) to the entire structure or a constant partial FS to a particular geotechnical variable is applied. The present paper aims at quantifying these uncertainties and proposes partial risk factors based upon the variations of geotechnical random variables. For this purpose, a gravity retaining wall is analyzed by pseudo-dynamic method of analysis against sliding and overturning modes of failure. The backfill and foundation soil properties are treated as random variables and the effect of their variation on stability of the wall for various earthquake conditions is investigated. Probability of Failure (P f ) for the two modes is calculated by Monte Carlo Simulation. Sensitivity analysis of each random variable is carried out by F-Test analysis to analyze the impact of the random variables on the failure modes. Finally, these two are combined mathematically to produce a modification factor called the Probabilistic Risk Factor (R f ) for each random variable. It is observed that apart from the seismic horizontal and vertical pseudo-dynamic coefficients Q h (t) and Q v (t), the variation in friction angle of backfill soil (φ 1 ) and cohesion of foundation soil (c 2 )are the major influential geotechnical parameters in stability of the gravity retaining wall. If the variation of internal angle of friction of backfill and foundation soil exceeds approximately 7–8%, the structure needs to be modified for stability requirements. Similarly, the dimension of the structure needs to be increased if COV of c 2 exceeds 20% to maintain stability. Parametric studies are carried out for different combinations of vertical and horizontal seismic acceleration coefficients, and risk factor based approach is applied in each case.